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Radial distribution probability

  • #1

Homework Statement


When I'm trying to find the probability of finding an electron within a sphere of a certain radius, do i integrate the radial distribution probability function with respect to r from 0 to infinity? My book says the product of the radial distribution function times dr would give the probability, but I always thought you had to integrate it.


Homework Equations


n/a just looking for a simple answer to my question... i didnt show the hw problem cos i wanna do it myself i just want this question answered.

The Attempt at a Solution


I've attempted the problem, i just integrated and I wanna know if you should integrate.
 

Answers and Replies

  • #2
kuruman
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The probability of finding the particle in a shell of thickness dr having radius r is

[tex]dP=|\psi|^2\:4\pi r^2dr[/tex]

The probability of finding the particle anywhere within a sphere of radius R is

[tex]P=\int^R_0 |\psi|^2\:4\pi r^2dr[/tex]

Does this help?
 
  • #3
yes! helps a ton! Thank you.
 
  • #4
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Notice that [tex]4\pi r^{2}[/tex] is the area of the surface of a sphere. This factor looks like that because you only have radial distribution, independent of azimuthal direction,
while if your wavefunction looks like [tex]\psi(r,\theta,\phi)[/tex] things will get a little more complicated, and will involve additional integrations.
 

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